Data Summary and Presentation

 

 

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Topics: Chapter 2 (Data Summary and Presentation)

 

  • Remember I cannot open documents in .pages format. If you are working on an Apple product, you must convert to .pdf or .docx before submitting your file.
  • Solutions to homework must be computer generated (Excel or Minitab).
  • Identify your answers clearly.
  • The last few pages of this document provide some instructions about using Excel for some of the exercises.
  • Answer all sub questions (if any) of a problem for full credit for that problem.
  • All questions carry equal points.
  • Data sets for the homework exercises can be found in the Homework tab on Blackboard in an Excel file called “ENGR2080 Chapter 2 Data Sets for Homework 1”.
  • Homework will be submitted on Blackboard. Any assignment submitted other than the indicated place on Blackboard may not receive credit.
  • Unless prior arrangements have been made, any homework turned in late will receive 10% penalty per class period.

 

Exercise 2-6 on page 28        (2 points)

 

Preventing fatigue crack propagation in aircraft structures is an important element of aircraft safety. An engineering study to investigate fatigue crack in n = 9 cyclically loaded wing boxes reported the following crack lengths (in mm):  2.13, 2.96, 3.02, 1.82, 1.15, 1.37, 2.04, 2.47, and 2.60. Calculate the sample average and sample standard deviation. Construct a dot diagram of the data, including a title for the chart.

 

Exercise 2-14 on page 33      (2 points)

 

The shear strengths of 100 spot welds in titanium alloy follow (and are posted in the Excel spreadsheet). Construct a stem-and-leaf diagram for the weld strength data and comment on any important features that you notice.

 

 

5408

5431

5475

5442

5376

5388

5459

5422

5416

5435

5420

5429

5401

5446

5487

5416

5382

5357

5388

5457

5407

5469

5416

5377

5454

5375

5409

5459

5445

5429

5463

5408

5481

5453

5422

5354

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5406

5444

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5447

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5384

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5454

5453

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5427

5421

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5425

5388

5388

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5481

5387

5440

5482

5406

5401

5411

5399

5431

5440

5413

5406

5342

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5420

5458

5485

5431

5416

5431

5390

5399

5435

5387

5462

5383

5401

5407

5385

5440

5422

5448

5366

5430

5418

 

 

Exercise 2-20 on page 34      (2 points)

 

Find the median, the quartiles, and 5th and 95th percentiles for the weld strength data in Exercise 2-14.

 

 

Exercise 2-26 on page 39      (2 points)

 

Construct a cumulative frequency plot and histogram for the weld strength data from Exercise 2-14.

 

NOTE:  The book suggests (a) Use 8 bins and (b) Use 16 bins and compare with part (a). If you are using a software tool like MINITAB where you can specify the number of bins, this is relatively simple. As an alternative, if you are working in Excel, you might let Excel choose the bins and then try your hand at specifying particular bins and compare the results of the two efforts.

 

 

Exercise 2-33 on page 40      (2 points)

 

The following data are the joint temperatures of the O-rings (oF) for each test firing or actual launch of the space shuttle rocket motor (from Presidential Commission on the Space Shuttle Challenger Accident, Vol. 1, pp.129-131):  84, 49, 61, 40. 83, 67, 45, 66, 70, 69, 80, 58, 68, 60, 67, 72, 73, 70, 57, 63, 70, 78, 52, 67, 53, 67, 75, 61, 70, 81, 76, 79, 75, 76, 58, 31.

  • Compute the sample mean and sample standard deviation.
  • Find the upper and lower quartiles of temperature.
  • Find the median.
  • Set aside the smallest observation (31 oF) and recompute the quantities in parts (a), (b), and (c). Comment on your findings. How “different” are the other temperatures from this smallest value?
  • Construct a box plot of the data and comment on the possible presence of outliers.

 

 

Exercise 2-54 on page 53      (2 points)

 

To investigate fuel efficiency, the following data were collected.

 

MPG

y

Weight x1 Horse-power x2 MPG

y

Weight x1 Horse-power x2
29.25 2464 130 17.00 4024 394
21.00 3942 235 17.00 3495 294
32.00 2604 110 18.50 4300 362
21.25 3241 260 16.00 4455 389
26.50 3283 200 10.50 3726 485
23.00 2809 240 12.50 3522 550

 

  • Create two scatter diagrams of the data. What do you anticipate will be the sign of each sample correlation coefficient?
  • Compute and interpret the two sample correlation coefficients.

 

 

 

If you are not familiar with Excel, here is a procedure you can use to calculate the sample mean and standard deviation:

  1. In a new Excel worksheet, type Crack Length in mm, or other appropriate title, in cell A1.
  2. Enter the data in a single column in cell A2 through A10. You can enter the data manually or copy it from the appropriate exercise in the spreadsheet called “Chapter 2 Data Sets”.
  3. In cell A11, key Mean =
  4. In cell B11, key =AVERAGE(A2..A10). Excel uses average for the arithmetic mean.
  5. From the Home tab, use the Decrease Decimal icon to round B11 to one decimal place.
  6. In cell A12, key Standard Deviation =
  7. In cell B12, key =STDEV(A2..A10).
  8. From the Tool Bar, use the Decrease Decimal icon to round B12 to one decimal place.

 

 

Here is a procedure you can use to construct a dot plot.

  1. Enter the number 1 in cells B2 through B10.
  2. Highlight cells A2 through B10. On the Insert tab, click Recommended Charts, select XY (Scatter), and click OK.
  3. Click on the Chart Title box and type Crack Length (in mm) or other appropriate title.
  4. Click on the chart to make the plus sign appear to the upper right of the chart. Click on the plus sign. In the Chart Elements box, click on the arrow to the right of Axes, and deselect Primary Vertical.